Asymptotic expansion in the central limit theorem for quadratic forms

Journal of Mathematical Sciences

Volumn 147, Issue 4, 2007, Pages 6891-6911

  Gotze F ^a   Tikhomirov, A N ^b   Yurchenko, V A ^b  

^a BIELEFELD UNIVERSITY   (Germany)

^b SYKTYVKAR STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36049052572     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/s10958-007-0512-8     Document Type: Article

References (16)

1. I. B. Alberink and V. Bentkus, "Bounds for the concentration of asymptotically normal statistics," Acta Appl. Math., 58, 11-59 (1999).
2. I. B. Alberink and V. Bentkus, "Berry-Esseen bounds for von Mises and U-statistics," Preprint 00-011, Universität Bielefeld (2000).
3. V. Bentkus and F. Götze, "Optimal rate of convergence in the CLT for quadratic forms," Ann. Probab., 24, 466-490 (1996).
4. V. Bentkus and F. Götze, "Optimal bounds in non-Gaussian limit theorems for U-statistics," Ann. Probab., 27, 454-521 (1999).
5. V. Bentkus, F. Götze, and W. R. van Zwet, "An Edgeworth expansion for symmetric statistics," Ann. Statist., 25, 851-896 (1997).
6. R. Fox and M. S. Taqqu, "Central limit theorems for quadratic forms in random variables having long-range dependence," Probab. Theor. Relat. Fields, 74, 312-340 (1987).
7. L. Giraitis and M. S. Taqqu, "Limit theorem for bivariate Appell polynomials. I, Central limit theorems," Probab. Theor. Relat. Fields, 107, 359-381 (1997).
8. F. Götze, "Asymptotic expansion for bivariate von Mises functionals," Z. Wahrsh. verw. Geb., 50, 333-355 (1979).
9. F. Götze, "Expansion for von Mises functionals," Z. Wahrsh. verw. Geb., 65, 599-625 (1984).
10. F. Götze and A. N. Tikhomirov, "Asymptotic distribution of quadratic forms," Ann. Probab., 27, 1072-1098 (1999).
11. F. Götze and A. N. Tikhomirov, "Asymptotic distribution of quadratic forms and application," J. Theor. Probab. 15, 439-491 (2002).
12. W. Hoeffding, "A class statistics with asymptotically normal distributions," Ann. Math. Statist., 19, 293-325 (1948).
13. P. Lancaster, Theory of Matrices, Academic Press (1969).
14. V. V. Petrov, Limit Theorems for Sums of Independent Random Variables, Springer-Verlag (1995).
15. R. Pike, "Spacings," J. R. Statist. Soc., B 27, 395-449 (1965).
16. A. N. Tikhomirov, "On the accuracy of the normal approximation of the probability of sums of weakly dependent Hilbert-space-valued random variables hitting a ball," Theory Probab. Appl., 36, 738-751 (1991).